The input data is assumed to be non-negative tensor. NTD decompose the tensor to the dense core tensor (S) and low-dimensional factor matices (A).
NTD(X, M=NULL, pseudocount=.Machine$double.eps, initS=NULL, initA=NULL,
fixS=FALSE, fixA=FALSE, L1_A=1e-10, L2_A=1e-10,
rank = rep(3, length=length(dim(X))),
modes = seq_along(dim(X)),
algorithm = c("Frobenius", "KL", "IS", "Pearson", "Hellinger", "Neyman",
"HALS", "Alpha", "Beta", "NMF"), init = c("NMF", "ALS", "Random"),
nmf.algorithm = c("Frobenius", "KL", "IS", "Pearson", "Hellinger", "Neyman",
"Alpha", "Beta", "ALS", "PGD", "HALS", "GCD", "Projected", "NHR", "DTPP",
"Orthogonal", "OrthReg"),
Alpha = 1,
Beta = 2, thr = 1e-10, num.iter = 100, num.iter2 = 10, viz = FALSE,
figdir = NULL, verbose = FALSE)S : K-order tensor object, which is defined as S4 class of rTensor package. A : A list containing K factor matrices. RecError : The reconstruction error between data tensor and reconstructed tensor from S and A. TrainRecError : The reconstruction error calculated by training set (observed values specified by M). TestRecError : The reconstruction error calculated by test set (missing values specified by M). RelChange : The relative change of the error.
K-order input tensor which has I_1, I_2, ..., and I_K dimensions.
K-order mask tensor which has I_1, I_2, ..., and I_K dimensions. If the mask tensor has missing values, specify the element as 0 (otherwise 1).
The pseudo count to avoid zero division, when the element is zero (Default: Machine Epsilon).
The initial values of core tensor which has I_1, I_2, ..., and I_K dimensions (Default: NULL).
A list containing the initial values of K factor matrices (A_k, <Ik*Jk>, k=1..K, Default: NULL).
Whether the core tensor S is updated in each iteration step (Default: FALSE).
Whether the factor matrices Ak are updated in each iteration step (Default: FALSE).
Paramter for L1 regularitation (Default: 1e-10). This also works as small positive constant to prevent division by zero, so should be set as 0.
Paramter for L2 regularitation (Default: 1e-10).
The number of low-dimension in each mode (Default: 3 for each mode).
The vector of the modes on which to perform the decomposition (Default: 1:K <all modes>).
NTD algorithms. "Frobenius", "KL", "IS", "Pearson", "Hellinger", "Neyman", "HALS", "Alpha", "Beta", "NMF" are available (Default: "Frobenius").
NMF algorithms, when the algorithm is "NMF". "Frobenius", "KL", "IS", "Pearson", "Hellinger", "Neyman", "Alpha", "Beta", "ALS", "PGD", "HALS", "GCD", "Projected", "NHR", "DTPP", "Orthogonal", and "OrthReg" are available (Default: "Frobenius").
The initialization algorithms. "NMF", "ALS", and "Random" are available (Default: "NMF").
The parameter of Alpha-divergence.
The parameter of Beta-divergence.
When error change rate is lower than thr1, the iteration is terminated (Default: 1E-10).
The number of interation step (Default: 100).
The number of NMF interation step, when the algorithm is "NMF" (Default: 10).
If viz == TRUE, internal reconstructed tensor can be visualized.
the directory for saving the figure, when viz == TRUE (Default: NULL).
If verbose == TRUE, Error change rate is generated in console windos.
Koki Tsuyuzaki
Yong-Deok Kim et. al., (2007). Nonnegative Tucker Decomposition. IEEE Conference on Computer Vision and Pattern Recognition
Yong-Deok Kim et. al., (2008). Nonneegative Tucker Decomposition With Alpha-Divergence. IEEE International Conference on Acoustics, Speech and Signal Processing
Anh Huy Phan, (2008). Fast and efficient algorithms for nonnegative Tucker decomposition. Advances in Neural Networks - ISNN2008
Anh Hyu Phan et. al. (2011). Extended HALS algorithm for nonnegative Tucker decomposition and its applications for multiway analysis and classification. Neurocomputing
plotTensor3D
tensordata <- toyModel(model = "Tucker")
out <- NTD(tensordata, rank=c(2,2,2), algorithm="Frobenius",
init="Random", num.iter=2)
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